Ciro Santilli @cirosantilli 35

A young Ciro Santilli really liked this game, the way it makes you feel.

To see that the real projective plane is not simply connected space, considering the lines through origin model of the real projective plane, take a loop that starts at $(1,0,0)$ and moves along the $y=0$ great circle ends at $(-1,0,0)$.

Note that both of those points are the same, so we have a loop.

Now try to shrink it to a point.

There's just no way!

From Henry V: www.poetryfoundation.org/poems/56972/speech-once-more-unto-the-breach-dear-friends-once-more

The discovery of the photon was one of the major initiators of quantum mechanics.

Light was very well known to be a wave through diffraction experiments. So how could it also be a particle???

This was a key development for people to eventually notice that the electron is also a wave.

This process "started" in 1900 with Planck's law which was based on discrete energy packets being exchanged as exposed at On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).

This ideas was reinforced by Einstein's explanation of the photoelectric effect in 1905 in terms of photon.

In the next big development was the Bohr model in 1913, which supposed non-classical physics new quantization rules for the electron which explained the hydrogen emission spectrum. The quantization rule used made use of the Planck constant, and so served an initial link between the emerging quantized nature of light, and that of the electron.

The final phase started in 1923, when Louis de Broglie proposed that in analogy to photons, electrons might also be waves, a statement made more precise through the de Broglie relations.

This event opened the floodgates, and soon matrix mechanics was published in quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), as the first coherent formulation of quantum mechanics.

It was followed by the Schrödinger equation in 1926, which proposed an equivalent partial differential equation formulation to matrix mechanics, a mathematical formulation that was more familiar to physicists than the matrix ideas of Heisenberg.

Inward Bound by Abraham Pais (1988) summarizes his views of the main developments of the subjectit:

Bibliography:

These are the key mathematical ideas to understand!!

There are actually a few formulations out there. By far the dominant one as of 2020 has been the Schrödinger picture, which contrasts notably with the Heisenberg picture.

Another well known one is the de Broglie-Bohm theory, which is deterministic, but non-local.

Quantum superposition is really weird because it is fundamentally different than "either definite state but I don't know which", because the superposition state leads to different measurements than the non-superposition state.

Examples:

Mostly interpreter of songs written by others. But she's just too amazing, many of her interpretations are better than the original.

God, even Ciro Santilli is slightly shocked by her death, which happened before he was born, can you imagine it at the time? She was MPB's golden girl...

Once upon a time in the 2010's, Ciro Santilli went to an artsy theatre venue in the suburbia of Paris, dragged by his wife then girlfriend of course.

In the venue, there was a politician, who was doing his best to show how much they supported the arts, and there were of course the artists, involved in the play.

The politician would see a political power score on top of every person's head, and would spend an amount of time talking to each person exactly proportional to that score. This meant basically one sentence to us. The words themselves didn't really matter of course, only the time spent, they just have to produce nice sounds.

One of the artists however, and he seemed quite important in the production, for some reason spent a huge amount of time speaking to us. The score the artist saw on our heads was of love, or how interested we were in the art.

This is quite in-depth, pretty good.

Unrelated to the Khan Academy.

Falls a bit too much on the basic side of the the missing link between basic and advanced.

YouTube channel: www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA

Does have some gems worth looking at. But generally always too superficial as can be expected from any self-sufficient YouTubber.

It is important to note that due to horizontal gene transfer, the early days of life, and still bacteria to this day due to bacterial conjugation, are actually a graph and not a tree, see also: Figure "Graph of life".

Definitely have a look at: coral of life representations.